def initialize_LR(self):
# initialize the Lpart and Rpart
first_LR = []
first_LR.append(np.ones((1, 1, 1, 1)))
second_LR = []
second_LR.append(np.ones((1, 1)))
for isite in range(1, len(self.cv_mps)):
first_LR.append(None)
second_LR.append(None)
first_LR.append(np.ones((1, 1, 1, 1)))
second_LR.append(np.ones((1, 1)))
if self.cv_mps.to_right:
path1 = [([0, 1], "abcd, efa->bcdef"),
([3, 0], "bcdef, gfhb->cdegh"),
([2, 0], "cdegh, ihjc->degij"),
([1, 0], "degij, kjd->egik")]
path2 = [([0, 1], "ab, cda->bcd"),
([1, 0], "bcd, edb->ce")]
for isite in range(len(self.cv_mps), 1, -1):
first_LR[isite - 1] = asnumpy(multi_tensor_contract(
path1, first_LR[isite], self.cv_mps[isite - 1],
self.a_oper[isite - 1], self.a_oper[isite - 1],
self.cv_mps[isite - 1]))
second_LR[isite - 1] = asnumpy(multi_tensor_contract(
path2, second_LR[isite], self.b_mps[isite - 1],
self.cv_mps[isite - 1]))
else:
path1 = [([0, 1], "abcd, aef->bcdef"),
([3, 0], "bcdef, begh->cdfgh"),
([2, 0], "cdfgh, cgij->dfhij"),
([1, 0], "dfhij, dik->fhjk")]
path2 = [([0, 1], "ab, acd->bcd"),
([1, 0], "bcd, bce->de")]
for isite in range(1, len(self.cv_mps)):
mps_isite = asxp(self.cv_mps[isite - 1])
first_LR[isite] = asnumpy(multi_tensor_contract(
path1, first_LR[isite - 1], mps_isite,
self.a_oper[isite - 1], self.a_oper[isite - 1],
self.cv_mps[isite - 1]))
second_LR[isite] = asnumpy(multi_tensor_contract(
path2, second_LR[isite - 1], self.b_mps[isite - 1],
mps_isite))
return [first_LR, second_LR]
def initialize_LR(self, direction):
first_LR = [np.ones((1, 1, 1))]
second_LR = [np.ones((1, 1, 1, 1))]
forth_LR = [np.ones((1, 1))]
for isite in range(1, len(self.cv_mpo)):
first_LR.append(None)
second_LR.append(None)
forth_LR.append(None)
first_LR.append(np.ones((1, 1, 1)))
second_LR.append(np.ones((1, 1, 1, 1)))
third_LR = copy.deepcopy(second_LR)
forth_LR.append(np.ones((1, 1)))
if direction == "right":
for isite in range(len(self.cv_mpo), 1, -1):
path1 = [([0, 1], "abc, defa -> bcdef"),
([2, 0], "bcdef, gfhb -> cdegh"),
([1, 0], "cdegh, ihec -> dgi")]
first_LR[isite - 1] = asnumpy(
multi_tensor_contract(
path1, first_LR[isite],
moveaxis(self.cv_mpo[isite - 1], (1, 2), (2, 1)),
self.a_oper[isite - 1], self.cv_mpo[isite - 1]))
path2 = [([0, 1], "abcd, efga -> bcdefg"),
([3, 0], "bcdefg, hgib -> cdefhi"),
([2, 0], "cdefhi, jikc -> defhjk"),
([1, 0], "defhjk, lkfd -> ehjl")]
path4 = [([0, 1], "ab, cdea->bcde"), ([1,
0], "bcde, fedb->cf")]
second_LR[isite - 1] = asnumpy(
multi_tensor_contract(
path2, second_LR[isite],
moveaxis(self.cv_mpo[isite - 1], (1, 2),
(2, 1)), self.b_oper[isite - 1],
self.cv_mpo[isite - 1], self.h_mpo[isite - 1]))
third_LR[isite - 1] = asnumpy(
multi_tensor_contract(
path2, third_LR[isite], self.h_mpo[isite - 1],
moveaxis(self.cv_mpo[isite - 1], (1, 2), (2, 1)),
self.cv_mpo[isite - 1], self.h_mpo[isite - 1]))
forth_LR[isite - 1] = asnumpy(
multi_tensor_contract(
path4, forth_LR[isite],
moveaxis(self.a_ket_mpo[isite - 1], (1, 2), (2, 1)),
self.cv_mpo[isite - 1]))
if direction == "left":
for isite in range(1, len(self.cv_mpo)):
path1 = [([0, 1], "abc, adef -> bcdef"),
([2, 0], "bcdef, begh -> cdfgh"),
([1, 0], "cdfgh, cgdi -> fhi")]
first_LR[isite] = asnumpy(
multi_tensor_contract(
path1, first_LR[isite - 1],
moveaxis(self.cv_mpo[isite - 1], (1, 2), (2, 1)),
self.a_oper[isite - 1], self.cv_mpo[isite - 1]))
path2 = [([0, 1], "abcd, aefg -> bcdefg"),
([3, 0], "bcdefg, bfhi -> cdeghi"),
([2, 0], "cdeghi, chjk -> degijk"),
([1, 0], "degijk, djel -> gikl")]
path4 = [([0, 1], "ab, acde->bcde"), ([1,
0], "bcde, bdcf->ef")]
second_LR[isite] = asnumpy(
multi_tensor_contract(
path2, second_LR[isite - 1],
moveaxis(self.cv_mpo[isite - 1], (1, 2),
(2, 1)), self.b_oper[isite - 1],
self.cv_mpo[isite - 1], self.h_mpo[isite - 1]))
third_LR[isite] = asnumpy(
multi_tensor_contract(
path2, third_LR[isite - 1], self.h_mpo[isite - 1],
moveaxis(self.cv_mpo[isite - 1], (1, 2), (2, 1)),
self.cv_mpo[isite - 1], self.h_mpo[isite - 1]))
forth_LR[isite] = asnumpy(
multi_tensor_contract(
path4, forth_LR[isite - 1],
moveaxis(self.a_ket_mpo[isite - 1], (1, 2), (2, 1)),
self.cv_mpo[isite - 1]))
return [first_LR, second_LR, third_LR, forth_LR]
def ones(shape, dtype=None):
if dtype is None:
dtype = backend.real_dtype
return Matrix(np.ones(shape), dtype=dtype)
def initialize_LR(self):
first_LR = [np.ones((1, 1, 1, 1))]
forth_LR = [np.ones((1, 1))]
for isite in range(1, len(self.cv_mpo)):
first_LR.append(None)
forth_LR.append(None)
first_LR.append(np.ones((1, 1, 1, 1)))
second_LR = copy.deepcopy(first_LR)
third_LR = copy.deepcopy(first_LR)
forth_LR.append(np.ones((1, 1)))
if self.cv_mpo.to_right:
for isite in range(len(self.cv_mpo), 1, -1):
cv_isite = self.cv_mpo[isite - 1]
dag_cv_isite = moveaxis(cv_isite, (1, 2), (2, 1))
path1 = [([0, 1], "abcd, efga -> bcdefg"),
([3, 0], "bcdefg, hgib -> cdefhi"),
([2, 0], "cdefhi, jikc -> defhjk"),
([1, 0], "defhjk, lkfd -> ehjl")]
path2 = [([0, 1], "ab, cdea->bcde"), ([1,
0], "bcde, fedb->cf")]
first_LR[isite - 1] = asnumpy(
multi_tensor_contract(path1, first_LR[isite], dag_cv_isite,
self.a_oper[isite - 1],
self.a_oper[isite - 1], cv_isite))
second_LR[isite - 1] = asnumpy(
multi_tensor_contract(path1, second_LR[isite],
dag_cv_isite, self.a_oper[isite - 1],
cv_isite, self.h_mpo[isite - 1]))
third_LR[isite - 1] = asnumpy(
multi_tensor_contract(path1, third_LR[isite],
self.h_mpo[isite - 1], dag_cv_isite,
cv_isite, self.h_mpo[isite - 1]))
forth_LR[isite - 1] = asnumpy(
multi_tensor_contract(
path2, forth_LR[isite],
moveaxis(self.b_mpo[isite - 1], (1, 2), (2, 1)),
cv_isite))
else:
for isite in range(1, len(self.cv_mpo)):
cv_isite = self.cv_mpo[isite - 1]
dag_cv_isite = moveaxis(cv_isite, (1, 2), (2, 1))
path1 = [([0, 1], "abcd, aefg -> bcdefg"),
([3, 0], "bcdefg, bfhi -> cdeghi"),
([2, 0], "cdeghi, chjk -> degijk"),
([1, 0], "degijk, djel -> gikl")]
path2 = [([0, 1], "ab, acde->bcde"), ([1,
0], "bcde, bdcf->ef")]
first_LR[isite] = asnumpy(
multi_tensor_contract(path1, first_LR[isite - 1],
dag_cv_isite, self.a_oper[isite - 1],
self.a_oper[isite - 1], cv_isite))
second_LR[isite] = asnumpy(
multi_tensor_contract(path1, second_LR[isite - 1],
dag_cv_isite, self.a_oper[isite - 1],
cv_isite, self.h_mpo[isite - 1]))
third_LR[isite] = asnumpy(
multi_tensor_contract(path1, third_LR[isite - 1],
self.h_mpo[isite - 1], dag_cv_isite,
cv_isite, self.h_mpo[isite - 1]))
forth_LR[isite] = asnumpy(
multi_tensor_contract(
path2, forth_LR[isite - 1],
moveaxis(self.b_mpo[isite - 1], (1, 2), (2, 1)),
cv_isite))
return [first_LR, second_LR, third_LR, forth_LR]
# -*- coding: utf-8 -*-
# Author: Jiajun Ren <*****@*****.**>
"""
construct the operator matrix in the MPS sweep procedure
"""
from functools import reduce
from collections import deque
from renormalizer.mps.backend import np, backend
from renormalizer.mps.matrix import Matrix, multi_tensor_contract, asxp, asnumpy
sentinel = np.ones((1, 1, 1), dtype=backend.real_dtype)
class Environ:
def __init__(self, mps, mpo, domain=None, mps_conj=None):
# todo: real disk and other backend
# idx indicates the exact position of L or R, like
# L(idx-1) - mpo(idx) - R(idx+1)
self._virtual_disk = {}
self._construct(mps, mpo, domain, mps_conj)
def _construct(self, mps, mpo, domain=None, mps_conj=None):
assert domain in ["L", "R", None]
if mps_conj is None:
mps_conj = mps.conj()
if domain is None:
self._construct(mps, mpo, "L", mps_conj)